"Kira" proclaiming her love for Odo would have been a big enough screw-up by itself, but her doing so only an episode after Vedek Bareil's death only makes it even more obvious that she's not the real deal. If Odo knows Kira well enough to know that she has no romantic feelings for him, then he knows she certainly wouldn't be interested in a rebound relationship right after the death of her previous love interest.
If you watch the episode, knowing the twist, a lot of the conversation could be seen as being turned into a way of subtly getting intelligence from Odo. For example, Odo and O’Brien’s friendships (and how long he would be out of the picture during a kayaking session).
If that had been the real Kira, then she probably would have taken offence at being told that Odo knows she's not in love with him due to knowing about human nature. Kira is a Bajoran, not a human, and is very proud of being Bajoran.
What would've happened if Odo HAD left "Kira" behind, as she urged him to? The Female Changeling, who had Kira trapped somewhere else, would probably have KILLED her to maintain the story.
"Kira" also hints that she's not Kira by not being able to reminisce about their escapades:
